4x^2+12x=9

Simple and best practice solution for 4x^2+12x=9 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4x^2+12x=9 equation:


Simplifying
4x2 + 12x = 9

Reorder the terms:
12x + 4x2 = 9

Solving
12x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 12x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 12x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-2.25 + 3x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 3x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 3x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 3x + x2 = 0 + 2.25
3x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
3x + x2 = 2.25

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2.25 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2.25 + 2.25

Combine like terms: 2.25 + 2.25 = 4.5
2.25 + 3x + x2 = 4.5

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.121320344 and -2.121320344.

Subproblem 1

x + 1.5 = 2.121320344 Simplifying x + 1.5 = 2.121320344 Reorder the terms: 1.5 + x = 2.121320344 Solving 1.5 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.121320344 + -1.5 x = 2.121320344 + -1.5 Combine like terms: 2.121320344 + -1.5 = 0.621320344 x = 0.621320344 Simplifying x = 0.621320344

Subproblem 2

x + 1.5 = -2.121320344 Simplifying x + 1.5 = -2.121320344 Reorder the terms: 1.5 + x = -2.121320344 Solving 1.5 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.121320344 + -1.5 x = -2.121320344 + -1.5 Combine like terms: -2.121320344 + -1.5 = -3.621320344 x = -3.621320344 Simplifying x = -3.621320344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.621320344, -3.621320344}

See similar equations:

| 4z-5= | | (x-1)*(x-3)=0 | | 9r+15=24+10r | | 4(x+2)=9x-7 | | 2x-3=35 | | 125+18h=200+12h | | 3a+2a=5 | | 3y+z= | | p-27=4p-15 | | 5(x-9)2=30 | | -2.5x+18-1.6x=5.7 | | 4m+18h-2m-3h= | | 8b=12b | | 5x=71+4x | | 2y^2-8y+5=0 | | 10y-4y+2f+3f= | | x^2-1.44=0 | | z^2-6z+8= | | 4X-2=-5X+16 | | 7(x-3)=2 | | 8w+2.6-3.6=63 | | 4x^2-34x+16=0 | | 12(391)=340x | | 4x^2+27x-14=10-2x | | x^3-6x^2+120x-224=0 | | 6b-8=8b-5b+1 | | 4x^2-18x-52=0 | | 3x-3=6+6 | | 3x+39=-39 | | 12=x+13 | | 3p=2p-75 | | 9(x-6)=5 |

Equations solver categories